Introducing Firm Heterogeneity into the GTAP

Model with an Illustration in the Context of the

Trans-Pacific Partnership Agreement

Zeynep Akgul∗, Nelson B. Villoria†, and Thomas W. Hertel‡

April 2014

(Preliminary and Incomplete)

∗Akgul is a Ph.D. candidate with the Department of Agricultural Economics, Purdue Uni-versity, West Lafayette, IN 47907, USA.†Villoria is a Research Assistant Professor of Agricultural Economics with the Center for

Global Trade Analysis, Purdue University, West Lafayette, IN 47907, USA.‡Hertel is a Professor of Agricultural Economics and the Executive Director of the Center

for Global Trade Analysis, Purdue University, West Lafayette, IN 47907, USA.

1

Contents

1 Introduction 4

2 Monopolistic Competition with Heterogeneous Firms 7

2.1 Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 Price Linkage . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Private Household Utility . . . . . . . . . . . . . . . . . . 10

2.2 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Fixed Costs . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.2 Value Added . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.3 Variable Costs . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.4 Productivity Draw . . . . . . . . . . . . . . . . . . . . . . 25

2.2.5 Markup Pricing . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.6 Firm Profits (Productivity Threshold) . . . . . . . . . . . 27

2.2.7 Average Productivity . . . . . . . . . . . . . . . . . . . . . 31

2.2.8 Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3 Endogenous Entry and Exit . . . . . . . . . . . . . . . . . . . . . 34

2.3.1 Industry Profit (Zero Profits) . . . . . . . . . . . . . . . . 35

2.3.2 Number of Firms . . . . . . . . . . . . . . . . . . . . . . . 37

3 Data Transformation 39

3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.1.1 Sourced Imports at Market Prices . . . . . . . . . . . . . . 40

3.1.2 Sourced Imports at Agent’s Prices . . . . . . . . . . . . . . 41

3.1.3 Trade Data . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2

4 Policy Application 45

5 Conclusions and Future Work 46

3

1 Introduction

Changes in trade flows in traditional Computable General Equilibrium models

(CGE) using the Armington specification (e.g. GTAP) are conditioned by pre-

existing trade shares thus capturing trade adjustments only at the intensive mar-

gin. This is at odds with the empirical trade literature that highlights the role of

extensive margin in explaining the expansion of trade following trade liberaliza-

tion episodes (Hummels and Klenow, 2005; Chaney, 2008). The firm heterogeneity

trade model proposed in the pioneering work of Melitz (2003) combines the inten-

sive margin with the extensive margin effects of trade liberalization capturing the

self-selection of firms into export markets based on their respective productivity

levels. The resulting framework is solidly supported by empirical evidence (Eaton

et al., 2004; Bernard et al., 2006). Including firm-level heterogeneity in a CGE

model can improve the ability of the model to trace out the trade expansion and

welfare implications of trade policy that were previously unexplored in traditional

models. In fact, it is shown that incorporating firm heterogeneity into standard

CGE models raises the gains from trade liberalization by a multiple of two in Zhai

(2008) and by a multiple of four in Balistreri et al. (2011).

There have recently been some important efforts to incorporate Melitz (2003)

into CGE modeling (Zhai, 2008; Balistreri and Rutherford, 2012; Dixon and Rim-

mer, 2011; Oyamada, 2013). However, a readily accessible GTAP implementation

with firm heterogeneity has not yet become available. Our paper addresses this

gap by incorporating Melitz-type firm heterogeneity into the GTAP model, cal-

ibrating it to the GTAP 8 Data Base and illustrating this framework with a

stylized scenario based on the Trans-Pacific Partnership (TPP), a regional free

trade agreement (FTA) currently under negotiation between the countries in the

4

Asia-Pacific region (Petri et al., 2012). A comparison with the Armington-based

standard GTAP model, as well as a GTAP-based model of monopolistic compe-

tition allows us to shed light on the new elements which the Melitz model brings

to bear on trade liberalization impacts.

One of the stylized facts shown by micro-level data is that within an industry

firms vary by their productivity, size, profitability, the number of markets served

and responses to trade shocks (Balistreri et al., 2011; Melitz and Trefler, 2012)

which is supported by the micro-level data (Bernard et al., 2003; Eaton et al.,

2004; Bernard et al., 2007). In particular, it is found that only some firms are

able to engage in exporting and exporters tend to be larger and more productive

than non-exporters (Balistreri et al., 2011; Bernard et al., 2003; Bernard and

Jensen, 1999). These stylized facts are captured by the framework in Melitz

(2003) who examines the intra-industry reallocation effects of international trade

in the context of a model with monopolistic competition and heterogeneous firms.

In his framework, opening the economy to trade or increasing the exposure to

trade generates a reallocation of market power within the domestic and export

markets based on the productivity differences of firms. In particular, firms with

higher productivity levels are induced to enter the export market; firms with

lower productivity levels continue to produce for the domestic market and the

firms with the lowest productivity levels are forced to exit the industry. These

inter-firm reallocations generate a growth in the aggregate industry productivity

which then increases the welfare gains of trade. This channel is a unique feature of

the firm heterogeneity model (Zhai, 2008). The main premise of the Melitz model

is that aggregate productivity can change even though there is no change in a

country’s production technology. As opposed to the allocative efficiency gains in

5

the firm heterogeneity model, aggregate productivity changes in traditional trade

models with homogeneous firms and Armington assumption are brought about by

changes in firm-level technology.

Melitz (2003) builds on Krugman’s (1980) monopolistic competition frame-

work to model trade; while it draws from Hopenhayn (1992) to model the endoge-

nous self-selection of heterogeneous firms. Likewise, we build on Swaminathan

and Hertel’s (1996) monopolistically competitive GTAP model where variety ef-

fects (changes in the number of firms – and hence distinct varieties offered) and

scale effects (changes in output per firm) are captured. We draw from the work of

Zhai (2008) in modeling firm heterogeneity and parsing productivity thresholds to

enter domestic and export markets and the calibration of fixed export costs, etc.

This allows us to endogenize aggregate productivity in the monopolistically com-

petitive sectors of the model, thereby capturing the intra-industry reallocation of

resources in the wake of trade liberalization.

Our framework differs from Zhai (2008) in two dimensions: (i) firm entry and

exit, and (ii) sunk entry costs. Specifically, Zhai (2008) assumes that the total

mass of potential firms in each sector is fixed. This simplification eliminates the

role of endogenous firm entry and exit; therefore, extensive margin effects pick

up only the changes in the shares of firms. In contrast, our model extends his

work by incorporating endogenous firm entry and exit behavior and tracing out

the direct effect of changes in the productivity threshold on entry and survival

in export markets. Another simplification of Zhai (2008) is the assumption of no

sunk-entry costs of production in the monopolistically competitive industry. In

contrast, our model incorporates fixed entry costs in the fashion of Swaminathan

and Hertel (1996) by assuming that they are only comprised of value added inputs

6

and calibrating them using the zero profits condition which arises from entry/exit

of firms. An additional contribution of our model is the decomposition of the

welfare implications of trade policy. This is an extension of the existing GTAP

welfare decomposition (Huff and Hertel, 2000), which now includes, in addition

to allocative efficiency and terms of trade effects, scale, variety, and endogenous

productivity effects derived from the firm heterogeneity model.

This paper is organized as follows: In Section 2 the theoretical framework

is laid out with details into the GTAP implementation. Section 3 describes the

data requirement for the firm heterogeneity model. In Section 4 we illustrate this

framework with a stylized trade liberalization scenario. Section 5 concludes the

paper.

2 Monopolistic Competition with Heterogeneous

Firms

This section describes the theoretical structure of the Melitz model and how it

is implemented into the GTAP. We build on Swaminathan and Hertel’s (1996)

monopolistically competitive GTAP model and draw from Zhai (2008) for firm

heterogeneity. In order to make this paper self-contained, we explain the signifi-

cant theoretical concepts adopted from Swaminathan and Hertel (1996) and Zhai

(2008) in the text. For details, we refer the reader to the associated papers or the

appendix.

One of the aims of this paper is to lay out the direct link between the theory

of Melitz-type CGE models and the firm heterogeneity GTAP model. In that

sense the notation adopted in this paper is similar to the literature. We explic-

7

itly show how to bring the theory into GEMPACK. We hope that this approach

makes it easier for the reader to follow the current literature and link it with our

methodology such that comparisons with other Melitz-type CGE models is easier.

A quick summary of the notation that we adopt in this paper is warranted.

In the sections that follow i denotes a commodity or an industry and r or s

denote a country or a region depending on the particular aggregation used. It

is important to highlight that we refer to three types of variables throughout

the paper; firm-level variables, average variables, and industry-level variables.

Firm-level variables are the variables associated with a different variety which are

indexed by ω or ϕ. Average variables are associated with representative variety

from the representative firm that operates at the average productivity level. This

follows from Melitz (2003) and is explained in more detail in the sections that

follow. At the industry-level we have the aggregate variables.

2.1 Demand

For the regional household we follow most of the standard GTAP model assump-

tions. The regional household collects and allocates all factor income and tax

as regional income according to a per capita aggregate utility function of the

Cobb-Douglas Form. The government utility function is also specified by the

Cobb-Douglas function. We also retain the non-homothetic utility structure of

private households via the Constant Difference of Elasticity (CDE) function. The

utility tree structure, so far, is the same as the standard model with homogeneous

goods produced in perfectly competitive industries. Differentiated varieties enter

the utility tree at the third nest which is where we have the sub-utility function for

composite commodities with a Constant Elasticity of Substitution (CES) form.

8

In the standard GTAP model, commodities are homogeneous and they are

produced in perfectly competitive industries in each region. Moreover, the stan-

dard GTAP model adopts Armington approach to import demand according to

which products are distinguished with respect to their country of origin. Thus,

at the border we have ‘composite imports’ which are imperfect substitutes for do-

mestic goods. In other words, composite imports compete with the domestically

produced commodities independent of their source country. In the monopolis-

tically competitive structure; however, firms within same industry of the same

region produce differentiated products. What matters to the consumers is not

where the variety originates, but what distinguishes it from the other products

of the industry. As opposed to an import-domestic decision, agents make a vari-

ety decision for the monopolistically competitive industry products. As a result,

sourced imports directly compete with the domestic varieties and agents face a

set of sourced varieties.

The implications of allowing for competition at the variety level is discussed

in more detail in Swaminathan and Hertel (1996). One important aspect they

emphasize is the need for a change in the structure of the database. Even though

the country of origin does not matter directly for consumers’ decision about which

variety to choose, they are affected by the number of varieties available in the

source country. Following Swaminathan and Hertel (1996) we source imports to

agents which requires the structural change in the data base. The transformation

of the data base is described in Section 3.

Another important aspect of allowing imported varieties for competing directly

with domestic varieties is the increase in the model size. In the standard model

agent demands are indexed by commodity and country. But, in the monopolistic

9

competition since imports are sourced, agent demands are indexed by commodity,

source and destination regions. Introducing this extra dimension increases the

number of equations and the related unknown variables to solve for.

2.1.1 Price Linkage

Changes in the data structure due to sourcing of imports is also reflected in the

price linkage. In the standard model, the prices that agents face are differentiated

between import and domestic prices. However, in the monopolistically compet-

itive model instead of discriminating between domestic and import prices, we

have prices that are indexed by source and destination. The price linkage in the

monopolistically competitive model is laid out in the Figure 2.1.1.

Figure 1: Price Linkage

2.1.2 Private Household Utility

Similar to the Krugman structure, we assume standard Dixit-Stiglitz preferences

over a continuum of differentiated varieties. The sub-utility function for the rep-

10

resentative household is given by:

Qis =

[∑r

α1σiirs

∫ω∈Ω

Qirs(ω)σi−1

σi dω

] σiσi−1

, (1)

where ω indexes each variety in the set of available varieties Ω, Qis is a CES

aggregate of all the varieties of commodity i demanded in region s, Qirs(ω) is the

demand for variety of commodity i produced in region r and sold in region s, αirs

is the Armington preference parameter reflecting consumers’ tendency for home

or imported products, and σi is the constant elasticity of substitution between

different varieties in the monopolistically competitive sectors (σi > 1). Each

variety is the product of a different firm. However, we assume that varieties are

symmetric for simplification. Therefore, from now on i indexes a representative

product of each commodity. This allows us to abstract from the continuum of

varieties and work with the representative household’s demand (see Appendix).

The sub-utility function becomes:

Qis =

[∑r

α1σiirsNirsQ

σi−1

σiirs

] σiσi−1

, (2)

where Qirs is representative household’s demand for a representative product i

sourced in region r and sold in region s, and Nirs is the total number of varieties

for product i in region s sourced from region r. In this framework there is a one-

to-one correspondence between firms and varieties. Hence Nirs also represents

the total number of firms in industry i that actively export from region r to s.

This brings us to a key differences between the firm heterogeneity GTAP model

and the monopolistically competitive GTAP model of Swaminathan and Hertel

(1996). In the monopolistically competitive model, it is assumed that all firms

11

that produce in the source country are active on the r-s export link. Therefore, the

sub-utility of the representative consumer depends on the total number of vari-

eties available for consumption in the monopolistically competitive GTAP model.

However, we should highlight that when firms are heterogeneous with respect to

their productivity levels, only a few firms that have high productivity levels afford

to actively export on every bilateral trade market. Therefore, consumers in the

destination region s only have access to the varieties of region r that are actually

being exported to s. The set of varieties that are sold on the r-s link is determined

endogenously in equilibrium. This will be explained in more detail in Section 2.3.

The average consumer in region s chooses Qirs that minimizes his expenditure:

minQirs

∑r

NirsQirsPirs

s.to Qis =

[∑r

α1σiirsNirsQ

σi−1

σiirs

] σiσi−1

,

where Pirs is the unit price of product i set by the representative firm with aver-

age productivity level (from now on ‘average firm’) operating on the r − s link.

Note that this average price is defined as gross of taxes and transportation costs.

The minimization problem yields the CES derived demand for the representative

product i sourced from region r as:

Qirs = αirsQis

[Pis

Pirs

]σi. (3)

By substituting the derived demand (equation 3) into the sub-utility function

(equation 2) and rearranging we can obtain the dual Dixit-Stiglitz price index for

12

product i in region s:

Pis =

[∑r

αirsNirsP1−σiirs

] 11−σi

. (4)

In sectors with differentiated goods, the Armington share parameter, αirs, is as-

sumed to be one. This assumption follows from Zhai (2008) and accounts for the

fact that bilateral trade patterns are determined by relative prices and the amount

of available varieties in the monopolistically competitive industries. On the other

hand, Nirs is assumed to be one in the standard GTAP model with Armington

assumption of national product differentiation. Hence the variance in bilateral

trade flows which cannot be explained by relative prices are contained in Arming-

ton share parameters (Hillberry et al., 2005). Hence incorporating monopolistic

competition into the GTAP model improves the ability of the model to explain

the variation in trade patterns by theory.

The rest of this section is devoted to the introduction of changes in the de-

mand structure into the GTAP model and the GEMPACK TABLO file. For this

purpose, we focus on equations (3) and (4).

Private Household’s Demand for Differentiated Products

We start with derived demand. Equation (3) gives the demand in region s for the

representative product i sourced from region r. However, it is only for an individ-

ual variety. To obtain the industry level demand, we need to aggregate across all

available varieties. One of the reasons why we aggregate is to minimize the addi-

tional information required from the dataset. As mentioned in Swaminathan and

Hertel (1996) the number, size and sales information in firm-level data is limited.

We follow Melitz (2003) to aggregate the firm-level information into industry-level

13

variables. The details of the Melitz-type aggregation is discussed later.

Aggregate derived demand in region s for all varieties of product i sourced

from r is given by:

Qirs = Nσiσi−1

irs Qirs. (5)

Aggregate price index in region s for all varieties of product i sourced from r is

given by:

Pirs = N1

1−σiirs Pirs. (6)

Using equations (3), and (6) in equation (5) we obtain the aggregate derived

demand on the r − s link as:

Qirs = Qis

[PisPirs

]σi, (7)

where αirs is assumed as one; thereby, is dropped for simplicity. Equation (7)

is the levels form of the aggregate demand in region s for product i sourced

from r. In GEMPACK we work with the linearized representations of equations;

therefore, we totally differentiate the equations we will incorporate into the firm

heterogeneity module.

Total differentiation of the aggregate demand yields:

qirs = qis − σi[pirs − pis], (8)

where the lower-case letters denote percentage changes in the associated upper-

case variables. Formally in TABLO:

14

EQUATION PHLDSRCDF

# Private HousehoLD demand for SouRCed DiFferentiated commodity #

# Equation names are identified by capitalized letters in comments

#

(all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

qdfps(i,r,s) = qp(i,s) - SIGMA(i) * [pps(i,r,s) - pp(i,s)];

This equation shows that percentage change in derived demand for differenti-

ated products still depends on the standard expansion and substitution effects.

However, we should highlight one significant difference. Imported varieties com-

pete directly with domestic varieties in the monopolistically competitive market.

Therefore, the substitution effect is the product of the constant elasticity of sub-

stitution between differentiated varieties, SIGMA(i), and the price of sourced dif-

ferentiated product relative to private household’s unit expenditure (or composite

price index), [pps(i,r,s) - pp(i,s)].

Private Household’s Composite Price Index for Differentiated Prod-

ucts

We follow the same method in incorporating the composite price index. Total

differentiation of equation (4) yields:

pis =∑r

αirsNirs

[PirsPis

]1−σi

pirs −1

σi − 1

∑r

αirsNirs

[PirsPis

]1−σi

nirs. (9)

Using equation (3) in equation (9) and rearranging we obtain:

pis =∑r

NirsQirsPirsQisPis

pirs −1

σi − 1

∑r

NirsQirsPirsQisPis

nirs, (10)

15

which can be simplified by defining the expenditure share as:

θirs =NirsQirsPirsQisPis

, (11)

where θirs is the expenditure share of all varieties of product i originating from

source r in total expenditure of all varieties from all sources in region s. In

TABLO:

FORMULA (all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

PTHETA(i,r,s) = VPAS(i,r,s) / sumk,REG, VPAS(i,k,s);

where VPAS(i,r,s) is the value of private household expenditure in region s at

agent’s price by source. The same applies to the computation of θirs for the

government and intermediate inputs. See Swaminathan and Hertel (1996) for

more details.

Substituting θirs (equation (11))into equation (10), the linearized representa-

tion of the composite price index equation becomes:

pis =∑r

θirspirs −1

σi − 1

∑r

θirsnirs. (12)

In TABLO:

EQUATION PHLDDFCOMPR

# Private HousehoLD PRice for DiFferentiated COMposite commodity #

(all,i,MCOMP_COMM)(all,s,REG)

pp(i,s) = sumr,REG, PTHETA(i,r,s) * ppsf(i,r,s)

- 1/[SIGMA(i) - 1] * vp(i,r,s) ;

Equation PHLDDFCOMPR shows that there are two things that distinguish price

index for differentiated products from that of homogeneous products. First of

all, data is sourced by agent. Hence agents face the average price of varieties

16

from each source region, ppsf(i, r, s). That applies to the expenditure shares

PTHETA(i, r, s), as well. In contrast, for homogeneous products, agents face a

composite of imported products. Secondly, we see the effect of variety on price

index via a variety index measure, vp(i, r, s). For simplicity, variety index is

defined in TABLO as a separate equation:

EQUATION PHLDVARIN

# Private HousehoLD VARiety INdex #

(all,i,MCOMP_COMM)(all,s,REG)

vp(i,r,s) = sumr,REG, PTHETA(i,r,s) * nx(i,r,s) + vpslack(i,r,s);

Equation PHLDVARIN shows that additional varieties on the r−s link raises the

variety index given the budget share. We introduce a slack variable, vpslack(i, r, s),

into this equation to allow for alternative closure options when there is no variety

effect (no entry and exit of new firms into the market).

As described by equation PHLDDFCOMPR, we see that an increase in the

variety index lowers the price index (SIGMA(i) > 1). As more and more varieties

are available for consumption, the amount of expenditure necessary to obtain a

unit of utility declines given prices.

Other Demand for Differentiated Products

The same changes apply to the government and intermediate input demand equa-

tions. The new equations introduced for the government module are GOVSRCDF,

GOVDFCOMPR, and GOVVARIN and for intermediate input are INDSRCDF,

INDDFCOMPR, and INDVARIN.

There are several issues related to intermediate input demands that need to

be clarified. As previously explained by Swaminathan and Hertel (1996), industry

derived demand equations have an extra dimension indexing the industry which

17

demands the intermediate input. With the extra dimension, sourced intermediate

input demand equations become four dimensional.

Firms are among the sources of demand and they, too, demand differentiated

varieties as intermediate inputs. We assume that firms are symmetric in their

demand for differentiated intermediate inputs. What matters for derived demand

equations is the nature of the intermediate input, not the nature of the industry

that demands the input. For instance, if a firm from a perfectly competitive mar-

ket demands differentiated intermediate inputs, then its derived demand equation

incorporates the effect of available varieties. Conversely, if a firm from a monop-

olistically competitive market demands homogeneous intermediate inputs, then

the derived demand equation it faces will have the standard form with Armington

assumption and composite import commodity formed at the border.

2.2 Production

Industry is characterized by a continuum of firms each producing a unique va-

riety. There is free entry and exit. Entry into an industry requires paying a

fixed entry cost which is thereafter sunk. This entry cost allows for increasing

returns to scale. Before entering the industry, firms are identical. Only after en-

tering the market firms draw their initial productivity parameter from a common

distribution and their productivity levels are revealed. Firms are heterogenous

in their productivity levels so that productivity is inversely related to marginal

costs. This firm-level heterogeneity means that production is carried out only by

firms that are productive enough to afford staying in the market given sunk-entry

costs. Compared to low-productivity firms, high-productivity firms produce more

output and earn higher profits by charging a lower price. Therefore, while low-

18

productivity firms are forced to exit the market, high-productivity firms expand

their market shares. Surviving firms have the choice to supply foreign markets

as well as satisfying home demand. To enter export markets, firms face another

set of fixed costs which are destination specific. Just as firms self-select into the

domestic market, they self-select into export markets based on their respective

productivity levels. Hence the distribution of firms is such that while the most

productive firms serve in the export markets, firms with lower productivity lev-

els supply only the domestic market, and the lowest-productivity firms exit the

industry.

This section discusses the production structure that characterize the monop-

olistically competitive industry with firm-level heterogeneity. We modify the ap-

proach of Swaminathan and Hertel (1996) in modeling mark-up pricing and cost-

structure. We follow Zhai(2008) to introduce endogenous productivity changes

into the framework.

2.2.1 Fixed Costs

Fixed costs are associated with the fact that differentiating a product within a

particular market is costly. Each firm targeting a niche has to invest in research

and development (R & D) to adapt its product to customer needs. Each new

market has different legislations and standards. Firms need to do market research

to learn about these rules and comply with them. These are fixed costs each firm

incurs to produce and sell its unique variety in a monopolistically competitive

industry. Upon entering the industry/market, these costs are sunk and do not

change with the production level. In this paper, we refer to the domestic market

entry cost as ‘sunk-entry cost’ and export market entry-cost as ‘fixed export cost’.

19

Following Swaminathan and Hertel (1996) we assume that all fixed costs (sunk-

entry and fixed export costs) are made up of primary input costs. The rationale

is that firms need capital to build the R & D labs, pay salaries to the employees

that work in R & D labs, doing market research, and marketing the new product.

These are all assumed to be primary factor costs. All of the primary factor costs

are referred to as Value Added Costs, VA(i,r), in the GTAP model. Hence VA(i,r)

is split into three parts: variable value-added, fixed value-added for the domestic

market and fixed value-added for the export market. We will examine the cost

structure in more detail later.

2.2.2 Value Added

Since differentiated industries require resources devoted to fixed costs to adapt

their products for new markets, demand for fixed value added is directly pro-

portional to the number of successful firms in the monopolistically competitive

market. This applies to both sunk-entry costs and fixed export costs. Formally

(in TABLO code):

EQUATION VAFDDEMAND

# monopolistically competitive industry DEMAND for Fixed Value-

Added #

(all,j,MCOMP_COMM)(all,s,REG)

qvafd(j,s) = n(j,s) ;

Sunk entry-costs are faced by all firms that enter the industry. We state that as

more firms enter the industry (as n(j, s) increases), the need for primary factors

increase, and demand for fixed value-added to cover sunk-entry costs, qvafd(j, s),

rises.

20

Some of the successfully producing firms in the industry self-select into export

markets based on their productivity levels and the fixed export costs they face.

Like with sunk-entry costs, demand for value-added used in fixed export costs is

directly proportional to the number of exporting firms on the specific bilateral

link. In TABLO code:

EQUATION VAFXDEMAND

# Value-Added DEMAND for Fixed eXport Costs #

(all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

qvafx(i,r,s) = nx(i,r,s) ;

Sunk-entry costs, and fixed export costs are the two components that make up

total demand for fixed value-added. To obtain the total demand for fixed value-

added we aggregate qvafd(j, s), and qvafx(i, r, s) based on their respective shares

in total fixed costs. In TABLO:

EQUATION VAFIX

# monopolistically competitive industry demand for FIXed Value-

Added #

(all,j,MCOMP_COMM)(all,s,REG)

qvaf(j,s) = [VAFD(j,s)/VAF(j,s)] * qvafd(j,s)

+ sum(k,REG,[VAFX(j,s,k)/VAF(j,s)] * qvafx(j,s,k)) ;

where V AFD(j, s)/V AF (j, s) is the share of sunk-entry cost in total fixed cost

and [V AFX(j, s, k)/V AF (j, s)] is the share of fixed export cost in total fixed cost.

In addition to the fixed component, there is also a variable component of the

value-added demand. The derived demand equation for variable value-added in

monopolistically competitive industry is similar to that of the perfectly competi-

tive industry and follows from the cost minimization problem in Gohin and Hertel

(2003). In TABLO:

21

EQUATION VAVDEMAND

# monopolistically competitive industry DEMAND for Variable Value-

Added #

(all,j,MCOMP_COMM)(all,s,REG)

qvav(j,s) + avav(j,s) = qo(j,s) - ao(j,s) ;

The variable value-added demand in industry j in region s, qvav(j, s), is propor-

tional to the industry output given productivity. If firms in the industry become

more productive, they use less variable value-added to produce a given level of

output. Hence demand for variable value-added declines.

Demand for total value added in industry j in region s, qva(j,s), is a weighted

summation of variable and fixed value-added demand based on respective weights

of variable and fixed value-added in total value-added. In TABLO:

EQUATION VATOT

# monopolistically competitive industry demand for TOTal Value-

Added #

(all,j,MCOMP_COMM)(all,s,REG)

qva(j,s) = [VAV(j,s)/VA(j,s)] * qvav(j,s)

+ [VAF(j,s)/VA(j,s)] * qvaf(j,s) ;

2.2.3 Variable Costs

Each firm minimizes its cost according to the following cost minimization problem:

minXijr

∑j

WijrXijr

s.t.Qjr = ϕjr

[∑i

δijrX

σj−1

σj

ijr

] σjσj−1

,

22

where Wijr is the price of input i employed in industry j of region r and Xijr is

the industry j demand for input i in region r, ϕjr is the productivity of industry j

in region r, and δijr is a distribution parameter that is used as input-augmenting

technical change in the GTAP model.

In contrast to Melitz (2003), production in our model requires multiple factors

(land, labor, capital, intermediate input). Therefore, we define productivity as

output per composite input according to equation (??).

The cost minimization problem yields the following unit cost, Cjr for product

j in region r:

Cjr =1

ϕjr

[∑i

δσjijrW

1−σjijr

] 11−σj

. (13)

Total differentiation of equation (13) yields:

cjr =∑i

βijr

[wijr −

σjσj − 1

δijr

]− ϕjr, (14)

where βijr is the cost share of factor i in industry j,and lowercase letters and

variables with hats denote percentage changes. We talk about what cost shares

entail later in this section. For details about this linearization see Gohin and

Hertel (2003).

Equation (14) is used to determine two types of costs: average variable cost

and average total cost. As explained before, average variable cost is a function of

the variable input prices such as intermediate inputs, and variable value-added.

In TABLO:

23

EQUATION AVERAGEVC

# AVERAGE Variable Cost #

(all,j,MCOMP_COMM)(all,r,REG)

VC(j,r) * avc(j,r)

= sumi,TRAD_COMM, VFA(i,j,r) * [pf(i,j,r) - af(i,j,r)]

+ VAV(j,r) * [pva(j,r) - avav(j,r)] - VC(j,r) * ao(j,r) ;

Note that the cost shares, βijr, in equation (14) correspond to V FA(i,j,r)V C(j,r)

for inter-

mediate inputs, and V AV (i,j,r)V C(j,r)

for the variable value-added in the code. The dis-

tribution parameters,σjσj−1

δijr, in equation (14) correspond to input-augmenting

technical change parameters, af(i, j, r) and avav(j, r), in the code.

As equation AVERAGEVC shows average variable cost does not vary with

the output level. On the other hand, average total cost of each firm change as a

result of two sources: (i) changes in firm output at constant input prices, or (ii)

changes in input prices at constant firm-level output. Following Swaminathan and

Hertel (1996) we focus on the latter and calculate changes in average total cost at

constant firm-level output. Average total cost in TABLO follows from equation

(14) as:

EQUATION SCLCONATC

# Average Total Cost at CONstant SCale #

(all,j,MCOMP_COMM)(all,r,REG)

VOA(j,r) * scatc(j,r)

= sumi,TRAD_COMM, VFA(i,j,r) * [pf(i,j,r) - af(i,j,r)]

+ VA(j,r) * [pva(j,r) - ava(j,r)] - VOA(j,r) * ao(j,r) ;

Since equation SCLCONATC determines average total cost at constant firm-level

output (constant scale), we adopt the convention of Swaminathan and Hertel

(1996) and refer to scatc(j, r) as the ‘scale constant average total cost’.

24

2.2.4 Productivity Draw

Firms are assumed to draw their productivity level, ϕ, from a Pareto distribution

with the lower bound ϕmin and shape parameter γ. The cumulative distribution

function of the Pareto distribution, G(ϕ), is:

G(ϕ) = 1− ϕ−γ, (15)

for ϕ ∈ [1,∞) where the lower bound ϕmin is assumed to be equal to one following

Zhai(2008). The corresponding density function, g(ϕ), is:

g(ϕ) = γϕ−γ−1. (16)

The shape parameter, γ, is an inverse measure of the firm heterogeneity. If it

is high, it means that the firms are more homogeneous. It is also assumed that

γ > σ − 1. This assumption is important in aggregation and it ensures that the

size distribution of firms has a finite mean (Zhai, 2008). The ex-ante probability

of successful entry is captured by:

1−G(ϕ∗) = (ϕ∗)−γ, (17)

where ϕ∗ is the threshold productivity level of producing in the market. This

definition of the ex-ante probability is used in all the sectoral aggregations over

individual varieties which we focus on in the following sections.

25

2.2.5 Markup Pricing

In the standard GTAP model each firm produces a homogeneous product under

constant returns to scale. The optimal pricing rule is that price equals marginal

cost. This is still the case for the perfectly competitive sectors in our model.

However, firms in the monopolistically competitive industry are price setters for

their particular varieties. Therefore, the optimal pricing rule for such a firm is to

charge a constant markup over marginal cost which is referred to as the mark-up

pricing rule given by:

Pir =σi

σi − 1

Cirϕir

, (18)

where Pir is the supply price of product i in the monopolistically competitive

sector in region r , σiσi−1

is the mark-up in industry i, Cir is the unit cost of

product i in region r, and ϕir is the average productivity of industry i in region r.

Firms in the perfectly competitive sectors do not have mark-ups and the industry

average productivity level is one in those sectors, , ϕir = 1.

Simplifying the mark-up rule in equation (18) we obtain:

PSir = MARKUPirMCir, (19)

where PSir is the supply price (excluding taxes and transportation costs), and

MCir is the marginal cost which correspond to Cirϕir

in equation (18). Since we

assume that production occurs under constant returns to scale, average variable

cost equals the constant marginal cost of production. Substituting the average

variable cost, AV Cir for MCir in equation (19) we obtain:

PSir = MARKUPirAV Cir. (20)

26

Total differentiation of (20) yields:

psir − avcir = markupir = 0 (21)

According to equation ((21)), in the monopolistically competitive industry, changes

in the producer price is directly proportional to changes in average variable cost

at constant mark-up. In TABLO:

EQUATION MKUPRICE

# MarKup pricing (with constant markup) #

(all,j,MCOMP_COMM)(all,r,REG)

psf(j,r) = avc(j,r) + mkupslack(j,r) ;

where psf(j, r) is the price received by average firm j in the monopolistically

competitive industry in region r. Industry level price requires aggregation over

all the firms in the industry. Equation MKUPRICE determines firm-level output,

qof(j, r), in the monopolistically competitive industry in region r. We include a

slack variable, mkupslack(j,r), in order to allow for alternative closures for different

trade policy applications where firm-level output is fixed. In such a scenario,

firm-level price would no longer equal average variable cost and the slack variable,

mkupslack(j,r), would absorb the difference between them.

2.2.6 Firm Profits (Productivity Threshold)

Each firm with productivity ϕirs makes the following profit from selling variety i

on the r − s link:

πirs(ϕ) = Qirs(ϕ)Pirs(ϕ)

(1 + tirs)−Qirs(ϕ)

Cirϕirs−WirFirs, (22)

27

for all r where the first component, Qirs(ϕ) Pirs(ϕ)(1+tirs)

, gives the total revenue, the

second component, Qirs(ϕ) Cirϕirs

, gives the variable cost and the third component,

WirFirs, gives the fixed cost of exporting on the r − s link. Substituting the

optimal demand and price for each variety, we obtain the maximized profit for

each firm as follows:

πirs =QirsP

σiirs

σi(1 + tirs)

[σi

σi − 1

(1 + tirs)Cirϕirs

]1−σi

−WirFirs. (23)

Firms in industry i export on the r − s link as long as the variable profit they

make cover the fixed cost of exporting. The firms with high productivity levels set

a lower price with a higher markup, produce more output; thereby, earn positive

profits. The only firm that exports on the r− s link and makes zero profits is the

marginal firm which produces at the threshold productivity level. At that thresh-

old variable profit only covers the export costs so the firm makes zero economic

profit. Thus, the zero-cutoff level of productivity for exporting on the r − s link

is where:

πirs(ϕ∗irs) = 0.

Solving equation (2.2.6) for the threshold productivity level yields:

ϕ∗irs =Cirσi − 1

[Pirs

σi(1 + tirs)

] σi1−σi

[WirFirsQirs

] 1σi−1

. (24)

Any firm that has a productivity level below ϕ∗irs cannot afford to produce in that

market, and therefore exits. On the other hand, any firm that has a productivity

28

level above ϕ∗irs stays in the market. Total differentiation of equation (24) yields:

ϕ∗irs = cir +σi

1− σi[pirs − tirs] +

1

σi − 1[wir + firs − qirs]. (25)

Equation (25) shows that the change in cutoff productivity level depends on the

unit cost of production, cir , price net of taxes and transportation costs, [pirs−tirs],

and the fixed cost per sale, [wir + firs − qirs]. The same equation is used to de-

termine the productivity threshold for the export market and for the domestic

market. The only difference is with respect to the fixed costs. For the domes-

tic threshold, sunk-entry costs per domestic sale is used, while for the export

threshold, fixed export costs per bilateral sale is used.

For the domestic market (r = s), equation (25) reduces to:

EQUATION PRODTRESHOLDD

# PRODuctivity THRESHOLD for the Domestic market#

(all,i,MCOMP_COMM)(all,r,REG)

aodf(i,r) = avc(i,r) - MARKUP(i,r) * ps(i,r)

+ [MARKUP(i,r) - 1] * [fdc(i,r) - qds(i,r)] ;

Note that fdc(i, r) is the sunk-entry cost which is a product of value added price

and fixed value-added inputs. In TABLO:

EQUATION FIXEDD

# FIXED Domestic costs (sunk-entry costs) #

(all,i,MCOMP_COMM)(all,r,REG)

fdc(i,r) = pva(i,r) + qvafd(i,r);

where qvafd(i, r) is the quantity of fixed value-added demanded by firms in indus-

try i in region r. Productivity threshold for the export market (r 6= s) according

to equation (25) is:

29

EQUATION PRODTRESHOLDX

# PRODuctivity THRESHOLD for the eXport market#

(all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

aoxf(i,r,s) = [1 - DELTA(r,s)]

* avc(i,r) - MARKUP(i,r) * ps(i,r)

+ [MARKUP(i,r) - 1] * [fxc(i,r,s) - qs(i,r,s)];

where DELTA(r, s) is called the Kronecker delta which is equal to one when

r = s. It is used in order to calculate the productivity threshold for just the export

market. Similar to the domestic sunk-entry cost, fixed export cost, fxc(i, r, s), is

a product of value added price and fixed value-added inputs. In TABLO:

EQUATION FIXEDX

# FIXED Export costs #

(all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

fxc(i,r,s) = pva(i,r) + qvafx(i,r,s);

where qvafx(i, r) is the quantity of fixed value-added demanded by firms in

industry i that export on the r − s link. Equation PRODTRESHOLDD and

PRODTRESHOLDX give us productivity thresholds at the firm-level for the do-

mestic and export markets, respectively. An increase in average variable cost

makes it more costly to enter a new market which in turn raises the productivity

threshold. This causes less productive firms to exit the market. If fixed export

cost per sale declines, the productivity threshold for the export market also de-

clines, given [MARKUP (i, r) − 1] > 0. Fixed costs are now spread over more

output such that it is less costly for lower productivity firms to engage in exports

on the r-s link.

30

2.2.7 Average Productivity

In equilibrium, firms that have productivity levels above the threshold, ϕ∗irs, pro-

duce for the market. Thus, the productivity of the industry is a weighted average

of the productivity levels of the firms that make the cut. The distribution of

productivity in equilibrium is given by

µ(ϕ) = g(ϕ)

1−G(ϕ∗)if ϕ ≥ ϕ∗

0 otherwise(26)

The distribution can be thought of as a conditional distribution of g(ϕ) on [ϕ∗,∞)

(meaning successful entry). This makes sense since the average productivity of

the sector will only be affected by the firms that are successful entrants. Now, we

can define the weighted average productivity level of the active firms on the r-s

link are as a function of the cutoff level of productivity as follows:

ϕirs(ϕ∗irs) =

[∫ ∞ϕ∗irs

ϕσi−1µ(ϕ)d(ϕ)

] 1σ−1

, (27)

=

[1

1−G(ϕ∗irs)

∫ ∞ϕ∗irs

ϕσi−1g(ϕ)d(ϕ)

] 1σi−1

, (28)

where ϕirs is a CES weighted average of the firm productivity levels and the

weights reflect the relative output shares of firms with different productivity lev-

els. Note that it is also independent of the number of successfully exporting firms.

Substituting ϕ∗irs in and applying the Pareto Distribution, the average productiv-

ity is found as:

ϕirs(ϕ∗irs) = ϕ∗irs

[γi

γi − σi + 1

] 1σi−1

, (29)

31

where γi > σi − 1. Total differentiation of equation (29) yields:

ϕirs = ϕ∗irs, (30)

where hat represents percentage change. Equation (30) shows thatchanges in aver-

age productivity is directly proportional to changes in the productivity threshold.

For the domestic market (r = s):

EQUATION AVEPRODD

# AVErage PRODuctivity for the Domestic market#

(all,i,MCOMP_COMM)(all,r,REG)

aods(i,r) = aodf(i,r);

For the export market (r 6= s),

EQUATION AVEPRODX

# AVErage PRODuctivity for the Export market #

(all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

aoxs(i,r,s) = aoxf(i,r,s);

Now that we have the average productivity for the domestic market and the

average productivity for export markets, we can calculate the average productivity

for the industry as a whole. It is a weighted average of productivity in the domestic

and export markets based on their relative market shares. In TABLO:

EQUATION AVEPRODS

# aggregate AVErage PRODuctivity of the whole Sector #

(all,i,MCOMP_COMM)(all,r,REG)

ao(i,r) = SHRDM(i,r)* aods(i,r)

+ sum(s,REG, SHRXMD(i,r,s) * aoxs(i,r,s))

+ prodslack(i,r);

where SHRDM(i,r) is the share of domestic sales of industry i in region r, and

SHRXMD(i,r,s) is the share of sales of industry i on the r − s link with respect

32

to total sales of the industry. According to equation AVEPRODS, aggregate pro-

ductivity rises with an increase in average productivity in the domestic market,

aods(i, r), average productivity in the export market, aoxs(i, r, s), or the respec-

tive shares of domestic and/or export markets in total sales.

If variable trade costs decline, profits of exporting firms increase and the pro-

ductivity threshold for the export market falls. This enables new and less pro-

ductive firms to enter the particular export market. Also, the existing exporting

firms will increase their sales and thereby their market shares as a result of lower

variable trade costs. The import competition in the domestic market forces less

productive domestic firms to shrink or exit. Therefore, while the most productive

firms increase their market shares, the least productive firms exit the market.

This raises the aggregate productivity of the industry.

2.2.8 Aggregation

As in Melitz (2003), the definition of average productivity is used to obtain the

aggregate variables of the model. Let us start with the aggregate price which is

given by

Pirs =

[∫ ∞0

Pirs(ϕ)1−σiNirsµ(ϕ)d(ϕ)

] 11−σ

. (31)

This is simplified by using the relationship between the firm with productivity

level ϕ and the average firm (see Appendix). Hence it reduces to

Pirs = N1

1−σiirs Pirs, (32)

33

where Pirs is actually the price of the representative firm that produces at the

average productivity level. Similar aggregations for demand and profit yields,

Qirs = Nσiσi−1

irs Qirs, (33)

Πirs = NirsΠirs. (34)

2.3 Endogenous Entry and Exit

In this section, we examine the zero profit condition and the endogenous entry and

exit of firms. All the firms that produce and export on the r-s link except for the

marginal firm earn positive profits. Thus, the average firm in the market makes

positive profits. Each firm stays in the business as long as all the profit they make

cover the sunk-entry cost of entering the market. In fact, Melitz (2003) states that

the firms forgo the entry cost due to the expectation of future positive profits.

Firms will enter the particular sector as long as the expected profits from each

potential market exceeds the firm level entry payment flow. At the industry level

the free entry/exit of firms fully exhaust the total profits such that the industry

makes zero profits.

Our framework for firm entry/exit differs from Zhai (2008). Specifically,

Zhai(2008) assumes that the total mass of potential firms in each sector is fixed.

This simplification eliminates the role of endogenous firm entry and exit; there-

fore, extensive margin effects pick up only the changes in the shares of firms.

In contrast, our model extends his work by incorporating endogenous firm entry

and exit behavior and tracing out the direct effect of changes in the productivity

threshold on entry and survival in export markets.

34

2.3.1 Industry Profit (Zero Profits)

Heterogeneous firms can make individual profits based on their respective pro-

ductivities (marginal costs). However, at the industry level there is zero profits

due to entry/exit of firms. Therefore, industry total revenue is fully exhausted by

total costs. An average firm makes the following total profits:

∑s

Πirs =∑s

[QirsPirs(1 + tirs)

− QirsCirϕirs

−WirFirs

]−WirHir, (35)

where Hir is the sunk-entry costs. 1 The total industry profit is just the average

profit adjusted by the number of successful entrants. Using the aggregation rule

in equation(34), the total industry profit is found as:

Πirs =∑s

NirsQirsPirs(1 + tirs)

−∑s

NirsQirsCirϕirs

−∑s

NirsWirFirs −NirWirHir. (36)

Hence the zero profit condition is:

∑s

NirsQirsPirs(1 + tirs)

=∑s

NirsQirsCirϕirs

+∑s

NirsWirFirs +NirWirHir. (37)

Using the GTAP notation, equation (37) is corresponds to:

V OA(j, r) =∑

i∈TRAD

V FA(i, j, r) + V AV (j, r)

+∑

s∈REG

V AFX(j, r, s) + V AFD(j, r), (38)

1Note that the unit cost for the sunk-entry costs and fixed export costs is the same, Wir,which is the composite price of value-added inputs. This follows from our assumption of allfixed costs are made up of primary factor costs.

35

where V OA(j, r) is the total revenue in industry j,∑

i∈TRAD V FA(i, j, r)+V AV (j, r)

is the total variable cost of production,∑

s∈REG V AFX(j, r, s) is the total fixed

cost of exporting, and V AFD(j, r) is the total sunk-entry costs in the industry.

Following Swaminathan and Hertel (1996), we totally differentiate equation (38)

and use the Envelope Theorem which yields:

V OA(j, r) ps(j, r) =∑

i∈TRAD

V FA(i, j, r) pf(i, j, r)

+ V A(j, r) pva(j, r)− V AF (j, r) qof(j, r), (39)

In TABLO:

EQUATION MZEROPROFITS

# ZERO pure PROFIT condition for firms in the Monopolistically comp

industry #

(all,j,MCOMP_COMM)(all,r,REG)

VOA(j,r) * ps(j,r) = VOA(j,r) * scatc(j,r)

- VAF(j,r) * qof(j,r) + zpislack(j,r) ;

The zero-profit equation captures the free-entry condition and determines the en-

dogenous number of firms in the industry. Note that the slack variable, zpislack(j, r),

is introduced in this equation to allow for alternative closures. For instance, if

there is no entry/exit in the industry, the number of firms in the industry is fixed.

In that case, the industry profit may be positive in the short-run. This is captured

by allowing the slack variable to be non-zero by endogenizing zpislack(j, r) in the

closure.

36

2.3.2 Number of Firms

This section focuses on two different free entry conditions; for the domestic market

and for the export market. As mentioned in section (2.3.1) domestic free entry and

exit is determined by the zero-profit condition. In fact, the zero-profit condition

dictates the change in output per firm, qof(j, s), which then determines the change

in the number of firms in the industry through the industry output equation. This

follows from Swaminathan and Hertel (1996). The total output in the industry

is a product of the successfully producing firms and the output of the individual

firm in the industry. It is given by the

Qir = NirQir, (40)

where Nir is the total number of firms in the industry, Qir is the output of the

representative firm in the monopolistically competitive industry. Note that we

assume symmetry in firm output. Total differentiation of 40 yields:

qir = nir + qir. (41)

In TABLO:

EQUATION INDOUTPUT

# INDustry OUTPUT in the monopolistically competitive industry #

(all,j,MCOMP_COMM)(all,r,REG)

qo(j,r) = qof(j,r) + n(j,r) ;

According to equation INDOUTPUT if output per firm rises less than the indus-

try output, then it means that new firms enter the industry. On the other hand,

if output per firm rises more than the industry output, then some firms must exit

37

the industry.

The entry and exit of firms in the domestic market is based on the interaction

between the industry and the average firm. The export market is a little different.

It directly depends on what happens in the productivity threshold of the export

market. The number of firms that successfully export is assumed to be given by

Nirs = Nir[1−G(ϕ∗irs)], (42)

where Nirs is the number of firms that export product i from region r to s, and

[1−G(ϕ∗irs)] is the ex-ante probability of successfully exporting on the r-s link. This

representation recognizes that not all firms in industry i are able to export on the

particular r-s link. Among all the firms in the industry only the firms that pass the

threshold productivity level of exporting are able to enter the export market, given

the productivity distribution. This representation follows Zhai (2008). However,

in our framework the number of exporting firms is endogenously determined by

this equation, while Zhai (2008) assumes that the total mass of potential firms in

each sector is fixed

Assuming Pareto distribution, equation (42) becomes:

Nirs = Nir(ϕ∗irs)−γi . (43)

Total differentiation yields

nirs = nir − γi(ϕ∗irs), (44)

where γi denotes the shape parameter of Pareto distribution. In TABLO:

38

EQUATION XFIRM

# number of eXporting FIRMs #

(all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

nx(i,r,s) = n(i,r) - SHAPE(i) * aoxf(i,r,s);

According to equation XFIRM, if the productivity threshold for the marginal firm

in the export market increases, some of the firms that did not make the cut will

be forced to exit the market. This is, of course, based on the heterogeneity of

the particular industry which is captured by the shape parameter of Pareto Pro-

ductivity. Recall that γi is an inverse measure of productivity. Therefore, as γi

increases, productivity becomes more uniform and firms become more homoge-

neous. In a more homogeneous industry, some firms must exit the export market

given constant productivity threshold and constant mass of firms since there are

more firms with similar productivity levels.

3 Data Transformation

In the monopolistic competition model imports are sourced by agent as mentioned

in the previous sections. The structure of the standard GTAP database is not

compatible with sourced imports. Therefore, in order to allow for sourced imports

and work with the monopolistically competitive GTAP model, we need to trans-

form the standard GTAP database. This section outlines the steps in making this

transformation following Swaminathan and Hertel(1996). Given the transformed

database, we turn to the additional data requirement of the firm heterogeneity

model such as fixed export costs.

39

3.1 Data

There are three steps to generate the monopolistically competitive data base:

• Sourcing of imports valued at importer’s market prices by agents

• Deriving the values of the sourced demands at agent’s prices

• Deriving the trade data

We summarize each step in this section for completeness purposes. For more

details, we refer the reader to Swaminathan and Hertel (1996).

3.1.1 Sourced Imports at Market Prices

In the standard GTAP database, consumption expenditure on domestic and im-

ported goods are given separately. For instance, the private household consump-

tion expenditure is VDPM(i,s) (on domestic goods) and VIPM(i,s) (on imported

goods). The first step is to transform agents’ domestic and import demands

into sourced demands valued at market prices. The transformation is outlined in

Figure 3.1.1. Sourcing out of aggregate imports consumed by the agent is done

Figure 2: Sourced Imports at Market Prices

through their market share. MSHRS(i,r,s) is defined as the market share of source

40

r in total imports of i by region s. The formula to calculate this share is as follows:

MSHRS(i, r, s) =V IMS(i, r, s)∑k V IMS(i, k, s)

, (45)

where VIMS(i,r,s) is the value of imports of i by source. DATAHETV1.TAB uses

the expenditure on imports and the market share to generate the expenditure for

sourced imports. If the source region, r, is the same as the destination region,

s, agents’ purchases of domestically produced goods are also added. The same

method is used for private households, government and firm intermediate input

demands. An example for private household is given as follows: for r 6= s

V PMS(i, r, s) = MSHRS(i, r, s) ∗ V IPM(i, s), (46)

and for r = s

V PMS(i, r, s) = MSHRS(i, r, s) ∗ V IPM(i, s) + V DPM(i, r, s). (47)

3.1.2 Sourced Imports at Agent’s Prices

The second step is to generate the sourced import demands valued at agents’

prices. The transformation we need is outlined in Figure 3.1.2.

We have already obtained the sourced imports at market prices in section 3.1.1

which together with the power of the tax generates sourced import demands value

at agent’s prices. We define the power of the average (ad volarem) tax on total

demand by an agent (TP(i,s), TG(i,s) and TF(i,j,s)). For private households it is

41

Figure 3: Sourced Imports at Agent’s Prices

calculated as follows:

TP (i, s) =V IPA(i, s) + V DPA(i, s)

V IPM(i, s) + V DPM(i, s). (48)

The same method is used for private households, government and firm intermedi-

ate input demands. Sourced purchases at agents’ prices is, then, just a product:

V PAS(i, r, s) = TP (i, s) ∗ V PMS(i, r, s) (49)

3.1.3 Trade Data

Trade data does not go through a complete change since it is already sourced. The

transformation is outlined in Figure 3.1.3. There are just two differences compared

to the standard GTAP trade data. The first one is the change in the notation.

Exports and Imports are renamed as “sales” and “demands”, respectively. The

second one is the fact that for r = s, aggregate domestic sales are taken into

account as well as the import sales due to market equilibrium. For instance, the

transformation of the value of sales by destination at market prices is as follows:

for r 6= s

V SMD(i, r, s) = V XMD(i, r, s), (50)

42

and for r = s

V SMD(i, r, s) = V XMD(i, r, s) + V DM(i, s), (51)

where VDM(i,s) is the value of aggregate domestic sales of i in s at market prices:

V DM(i, s) = V DPM(i, s) + V DGM(i, s) +∑j

V DFM(i, j, s). (52)

Figure 4: Trade Data

3.2 Calibration

Some of the information required in the firm heterogeneity model is not available

in the GTAP database such as the elasticity of substitution between varieties,

the shape parameter of Pareto distribution, data for sunk-entry costs and fixed

exporting cost. We take the elasticity of substitution between varieties (σi), and

the shape parameter of Pareto distribution (γi) from the literature. On the other

hand, we calibrate total fixed costs and fixed export costs. For the calibration of

total fixed costs we follow Swaminathan and Hertel (1996), while for the calibra-

tion of fixed export costs we follow Zhai (2008).

43

As explained before value added costs are composed of a fixed, VAF(i,r), and

a variable, VAV(i,r), part. Initial value for the fixed value-added is calibrated by

using mark-up pricing and market clearing equation. It follows that the share of

fixed costs in total costs is given by the following formula:

formula (all,i,MCOMP_COMM)(all,r,REG)

VAF(i,r) = VOA(i,r) * 1 - [1 / MARKUP(i,r)];

where 1σi

portion of total costs is fixed costs. The rest of the value-added costs

are attributed to variable value-added in the following fashion:

formula (all,i,MCOMP_COMM)(all,r,REG)

VAV(i,r) = VA(i,r) - VAF(i,r);

This follows directly from Swaminathan and Hertel (1996). Recall that in the

firm heterogeneity model fixed value-added costs, VAF(i,r), is split into the sunk-

entry costs, VAFD(i,r), and fixed export costs, VAFX(i,r,s). The initial value of

the fixed export costs is calibrated to the base year bilateral trade flows following

Zhai (2008). Solving the bilateral trade flow equation for fixed export costs yields:

NirsFirs =PirsQirs

(1 + tirs)

γi − σi + 1

σiγi. (53)

This caibration appears in the code as:

FORMULA (initial)(all,i,MCOMP_COMM)(all,r,REG)(all,s,REG)

VAFX(i,r,s) = [1 - DELTA(r,s)]

* VSMD(i,r,s) * 1 - [1 / (MARKUP(i,r)-1)]

* [1/SHAPE(i)] ;

where DELTA(r,s) is, again, the Kronecker delta which is equal to one when r = s.

Once fixed export costs are calibrated, sunk-entry cost is a residual in total fixed

44

costs. It appears in the code as follows:

FORMULA (all,i,MCOMP_COMM)(all,r,REG)

VAFD(i,r) = VAF(i,r) - sum(s,REG,VAFX(i,r,s));

4 Policy Application

In order to illustrate the usefulness of this model, we aggregate the GTAP v.8 data

base to 2 commodities (manufacturing, and non-manufacturing) and 3 regions

(USA, Japan, and ROW), wherein the manufacturing sector is treated as mo-

nopolistically competitive with heterogeneous firms, and the non-manufacturing

sector is treated as perfectly competitive/Armington. The aggregation adopted

is the same as in Swaminathan and Hertel(1996) for comparison purposes. The

program requires minor changes to run with a different aggregation. We elimi-

nate Japanese tariffs on the import of US manufacturing goods to illustrate the

workings of our model.

The direct effect of the tariff liberalization policy is a reduction in the price

of US manufactures in the Japanese market, an increase in the quantity of US

manufactures sales to Japan, a decrease in domestic sales and in the sales to

the ROW – results which are similar to those from the monopolistic competition

and firm heterogeneity models. A unique aspect of the firm heterogeneity model

is its ability to capture the impact of trade liberalization on marginal firms for

each source-destination link. In our example, the Japanese tariff cut reduces the

productivity threshold for successfully exporting on the US-Japan link (-1.6%).

With the lower tariff, US exporters obtain a larger market in Japan and sales to

Japan rise (22.6%). This reduces fixed export costs per unit of exports, capturing

45

scale effects in the export market and allowing the firms with lower productivity

to profitably export on the US-Japan link. Therefore, new US varieties enter the

Japanese market (13%). The productivity threshold for exports on the Japan-US

link also declines (-0.1%), but mostly due to the reduction in average variable

costs in Japan, as the cost of intermediate inputs falls.

The within industry firm reallocation extends to the domestic markets. The

productivity threshold of producing for the domestic market increases for the US

(0.03%) and Japan (0.1%). The rise in average variable cost and the sunk entry

cost per domestic sale makes it costly for the US firms to produce in the man-

ufacturing sector and reduces their profits; therefore, low-productivity firms exit

the industry (-0.04%). In contrast, the domestic productivity threshold increase

in Japan is driven by the decline in Japanese prices due to intensified competi-

tion. Trade liberalization, therefore, reallocates market share by shifting resources

towards more productive firms improving the aggregate productivity in the US

(0.02%) and Japan (0.04%). We also compare the change in the terms of trade

(TOT) across models. Standard GTAP model results demonstrate that there is

a shift in favor of the US, whereas TOT decline for Japan. But, the experiments

in monopolistic competition and firm heterogeneity models result in a smaller

improvement in the US TOT and magnify the decline in that of Japan.

5 Conclusions and Future Work

In this paper we discuss how to implement monopolistic competition with firm

heterogeneity into the GTAP model. Different from the standard GTAP model

with Armington specification, the firm heterogeneity module includes the effect of

new varieties in markets (extensive margin), the effect of scale economies, and the

46

effect of endogenous productivity. We build on Zhai (2008) for firm heterogeneity;

however, compared to his approach we incorporate endogenous firm entry/exit,

and we distinguish between sunk-entry costs, and fixed export costs.

The model is calibrated to GTAP (version 8.0) database. There are three

pieces of information not contained in the GTAP database that are needed in firm

heterogeneity approach: (i) the elasticity of substitution between varieties, (ii) the

shape parameter of the Pareto productivity distributions, and (iii) the magnitude

of fixed export costs. We adopt Zhai’s (2008) approach to calibrate fixed export

costs based on a gravity model of trade using bilateral trade flows. The elasticity

of substitution between varieties, and shape parameter of the productivity distri-

bution is taken from the literature. Model results in firm heterogeneity module

depends on the choice of substitution elasticity and shape parameter. For fu-

ture work, we aim to combine econometric work on model parameters with policy

analysis to obtain more robust results.

To illustrate the behavioral characteristics of the model, we analyze the effects

of eliminating Japanese tariffs on the import of US manufacturing goods under a

three region - two sector aggregation. This is a highly stylized FTA scenario in

TPP with the aim of laying out the mechanics of this Melitz-type GTAP model.

We observe that productivity threshold for the US-Japan export market reduces

mostly due to the reduction in fixed export costs per sale. This scale effect is the

dominant factor in threshold reduction and a subsequent increase in the number

of US manufacturing firms exporting in Japanese markets. This firm reallocation

in US-Japan link is in favor of lower-productivity firms. On the other hand, the

within firm reallocation in the domestic market is such that low-productivity firms

are forced to exit due to higher average variable costs. As a result of exit of firms

47

in the domestic market, the productivity of US manufacturing sector rises.

By incorporating monopolistic competition and firm heterogeneity, we are able

to capture and analyze the previously unobserved effects of trade agreements. The

question to ask at this point is whether these effects matter for trade policy impli-

cations. In other words, do we expand our insight by using a Melitz-type GTAP

framework over the traditional model with Armington assumption? An initial

comparison of model responses to tariff elimination across GTAP models with

Armington, Krugman, and Melitz specifications do not show significant variation

when the policy instrument is the tariff rate.

The main premise of the TPP agreement is to develop comprehensive, high-

quality rules in trade that harmonize standards and thereby reduce barriers to

trade. The variation in trade standards across regions force firms to incur sig-

nificant fixed export costs. Reduction in these costs are expected to generate

huge gains for the member countries. As a future work we aim to analyze a more

comprehensive TPP scenario with fixed export costs as the policy instrument.

The GTAP model with firm heterogeneity responds to fixed export cost reduc-

tions by changing industry productivity as a result of shifts in the export market

productivity thresholds which is unique to the firm heterogeneity framework.

A second goal in our future work is to discuss the welfare implications of TPP

under this new framework. There are three additional channels through which

trade liberalization yields welfare gains in the firm heterogeneity GTAP model;

namely, variety, scale, and productivity effects. We will focus on the welfare

response of the GTAP model to different policy instruments such as tariff, and

fixed export costs under Armington, Krugman and Melitz specifications.

48

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